Question: What's the first wrong statement in the proof below that $ \triangle EBC \cong \triangle EBD$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle DBE \cong \angle CFE$ $, \ $ $ \overline{BE} \cong \overline{EF}$ $, \ $ $ \angle BED \cong \angle CEF$ $, \ $ $ \overline{DE} \cong \overline{AC}$ $, \ $ $ \angle BDE \cong \angle ACB$ $, \ $ and $\ $ $ \angle DBE \cong \angle ABC$ Proof $ \triangle EFC \cong \triangle EBD$ because ASA $ \overline{CE} \cong \overline{DE}$ because corresponding parts of congruent triangles are congruent $ \overline{BE} \cong \overline{DF}$ because corresponding parts of congruent triangles are congruent $ \angle CBE \cong \angle BED$ because alternate interior angles are equal $ \triangle ABC \cong \triangle EBD$ because AAS $ \triangle EBC \cong \triangle EBD$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{DF} \cong \overline{BE}$ is the first wrong statement.